IIT-JEE Exam

A rectangular sheet of fixed perimeter with sides having their lengths in the ratio 8 : 15 is converted into an open rectangular box by folding after removing squares of equal area from all four corners. If the total area of removed squares is 100, the resulting box has maximum volume. Then the lengths of the sides of the rectangular sheet are
option
a) 24
b) 32
c) 45
d) 60

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IIT-JEE Other Question
For 3i^3 matrices M and N, which of the following statement(s) is (are) NOT correct ?
(A) NTMN is symmetric or skew symmetric, according as M is symmetric or skew symmetric
(B) MN, NM is skew symmetric for all symmetric matrices M and N
(C) MN is symmetric for all symmetric matrices M and N
(D) (adj M) (adj N) = adj(MN) for all invertible matrices M and N A pack contains n cards numbered from 1 to n. Two consecutive numbered cards are removed from the pack and the sum of the numbers on the remaining cards is 1224. If the smaller of the numbers on the removed cards is k, then k  20 equal to,
option
a) 5
b) 4
c) 3
d) 2